Nonlinear conductivity of the two-dimensional Wigner solid on the free surface of normal and superfluid He-3

The theory of nonlinear conductivity of the 2D Wigner solid (WS) formed on the surface of normal and superfluid He-3 is presented. We show that extremely strong damping of the Fermi-liquid He-3 greatly affects the dimple sublattice of surface displacements moving along with the WS, which induces the nonlinear conductivity of surface electrons long before the conventional Bragg-Cherenkov condition is achieved. Both the hydrodynamic and Iona mean-free-path regimes are considered in order to find the velocity induced transformation of the dimple sublattice and field-velocity characteristics of the WS. Depending on the regime of measurement the theory describes dynamic decoupling of the WS from surface dimples, or the field-velocity characteristics which has regions with negative differential conductivity.